MONTE-CARLO STUDY OF CLUSTER-DIAMETER DISTRIBUTION - AN OBSERVABLE TOESTIMATE CORRELATION LENGTHS

We report numerical simulations of two-dimensional q-state Potts model s with emphasis an a new quantity for the computation of spatial corre lation lengths. This quantity is the cluster-diameter distribution fun ction G(diam)(x), which measures the distribution of the diameter of s tochastically defined cluster. Theoretically it is predicted to fall o ff exponentially for large diameter x, G(diam alpha)exp(-chi/xi). wher e xi is the correlation length as usually defined through the large-di stance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models wit h q=10, 15, and 20 on large square lattices of size 300x 300, 120x 120 , and 80x 80, respectively, clearly confirm the theoretically predicte d behavior, Moreover, using this observable we are able to verify an e xact formula for the correlation length xi(d) lambda(beta(1)) in the d isordered phase at the first-order transition point beta(1) with an ac curacy of about 1%-2% for all considered values of q. This is a consid erable improvement over estimates derived from the large-distance beha vior of standard (projected) two-point correlation functions, which ar e also discussed for comparison.